Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904452 | Acta Mathematica Scientia | 2017 | 22 Pages |
Abstract
In this paper we study a fractional stochastic heat equation on
Rd(dâ¥1) with additive noise
ââtu(t,x)=dδ_α_u(t,x)+b(u(t,x))+WËH(t,x) where
dδ_α_ is a nonlocal fractional differential operator and
WËH is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d=1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Junfeng LIU, Ciprian A. TUDOR,